Solar radius and luminosity variations induced by the internal dynamo magnetic fields

Although the occurrence of solar irradiance variations induced by magnetic surface features (e.g., sunspots, faculae, magnetic network) is generally accepted, the existence of intrinsic luminosity changes due to the internal magnetic fields is still controversial. This additional contribution is expected to be accompanied by radius variations, and to be potentially significant for the climate of the Earth. We aim to constrain theoretically the radius and luminosity variations of the Sun that are due to the effect of the variable magnetic fields in its interior associated with the dynamo cycle. We have extended a one-dimensional stellar evolution code to include several effects of the magnetic fields on the interior structure. We investigate different magnetic configurations, based on both observational constraints and on the output of state-of-the-art mean field dynamo models. We explore both step-like and simply periodic time dependences of the magnetic field peak strength. We find that the luminosity and radius variations are in anti-phase and in phase, respectively, with the magnetic field strength. For peak magnetic field strengths of the order of tens of kilogauss, luminosity variations ranging between 10^{-6} and 10^{-3} (in modulus) and radius variations between 10^{-6} and 10^{-5} are obtained. Modest but significant radius variations (up to 10^{-5} in relative terms) are obtained for magnetic fields of realistic strength and geometry, providing a potentially observable signature of the intrinsic variations. Establishing their existence in addition to the accepted surface effects would have very important implications for the understanding of solar-induced long-term trends on climate.Comment: 18 pages, 7 figures; accepted for publication in Astronomische Nachrichte

Power Density Spectra of Gamma-Ray Bursts in the Internal Shock Model

We simulate Gamma-Ray Bursts arising from internal shocks in relativistic winds, calculate their power density spectrum (PDS), and identify the factors to which the PDS is most sensitive: the wind ejection features, which determine the wind dynamics and its optical thickness, and the energy release parameters, which give the pulse 50-300 keV radiative efficiency. For certain combinations of ejection features and wind parameters the resulting PDS exhibits the features observed in real bursts. We found that the upper limit on the efficiency of conversion of wind kinetic energy into 50-300 keV photons is $\sim$ 1%. Winds with a modulated Lorentz factor distribution of the ejecta yield PDSs in accord with current observations and have efficiencies closer to $10^{-3}$, while winds with a random, uniform Lorentz factor ejection must be optically thick to the short duration pulses to produce correct PDSs, and have an overall efficiency around $10^{-4}$.Comment: 6 pages, 4 figures, Latex, submitted to The Astrophysical Journal (05/04/99

Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and red giant stars. Under the assumption of local angular momentum conservation, the core contraction and envelope expansion occurring at the end of the main sequence would result in a much larger internal differential rotation than observed. This suggests that angular momentum redistribution must be taking place in the interior of these stars. Aims. We investigate the physical nature of the angular momentum redistribution mechanisms operating in stellar interiors by constraining the efficiency of post-main sequence rotational coupling. Methods. We model the rotational evolution of a 1.25 Msun star using the Yale Rotational stellar Evolution Code. Our models take into account the magnetic wind braking occurring at the surface of the star and the angular momentum transport in the interior, with an efficiency dependent on the degree of internal differential rotation. Results. We find that models including a dependence of the angular momentum transport efficiency on the radial rotational shear reproduce very well the observations. The best fit of the data is obtained with an angular momentum transport coefficient scaling with the ratio of the rotation rate of the radiative interior over that of the convective envelope of the star as a power law of exponent ~3. This scaling is consistent with the predictions of recent numerical simulations of the Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular momentum transport process whose efficiency varies during the stellar evolution through a dependence on the level of internal differential rotation is required to explain the observed post-main sequence rotational evolution of low-mass stars.Comment: 8 pages, 6 figures; accepted for publication in Astronomy & Astrophysic

Ground motion and stress accumulation driven by density anomalies in a viscoelastic lithosphere. Some results for the Apennines

SUMMARY We provide the analytical formulation for calculating the displacement and stress field forced by internal sources in a stratified, self-gravitating, viscoelastic earth. This model is specialized to study the rate of vertical motion and shear stress accumulation produced by lithospheric density anomalies. These sources are allowed to vary in the lateral direction. We show that sphericity plays a crucial role for elongated lithospheric anomalies while self-gravitation produces minor deviations from a gravitating Earth. When the model is applied to the Apennines we get, for lithospheric viscosity ranging between 10" and loz3 Pas, the subsidence of the plate underlying the active front of the overthrusting load to be around 0.5-1.0 mm yr-'. This is consistent with the amount of sedimentation in the Adriatic foredeep. The deformation pattern is very peculiar, with the largest subsidence localized beneath the active front of the topography. Our model enlightens the impact of discontinuities of tectonic phases on vertical motions in collision zones. If lithospheric viscosity is around 10'' Pa s, vertical motions decay drastically on time scales of 105yr if lateral migration of density anomalies comes to an end. For higher viscosities, deformation rates are maintained longer. This correlation between horizontal and vertical motions suggests that altimetric geodetic surveying along levelling lines of a few hundred kilometers can be an important tool to constrain the tectonics of the studied region. Results are also shown for vertical motions along a transect perpendicular to the Apennines, when the crustal structure inverted from Bouguer gravity data is considered. Analysis of the stress field induced by an overthrusting load shows that principal stress differences of a few bar (or a few tenths of MPa) can be accumulated on time scales of 102-103yr. These low values agree with the average stress drop of earthquakes in the Appalachians and northern Apennines where our modelling can be applied. We find that lateral density variations certainly contribute to intraplate stresses, but they are less efficient in triggering earthquakes than other mechanisms, such as transcurrent motions along active plate margins. Seismicity induced by lateral variations of crustal and lithospheric density must be moderate, characterized by long return times. These results are in agreement with the recorded seismicity in the northern Apennines where the largest earthquakes have return times of lo2 yr. If shear stress is forced by an overthrusting load, we find that the largest rate of stress accumulation in the crust is concentrated beneath the active front, close to the boundary with the ductile lithosphere. Discontinuities of tectonic phases play an important role in controlling the amount of shear stress due to density anomalies

Analysis of Temporal Features of Gamma Ray Bursts in the Internal Shock Model

In a recent paper we have calculated the power density spectrum of Gamma-Ray Bursts arising from multiple shocks in a relativistic wind. The wind optical thickness is one of the factors to which the power spectrum is most sensitive, therefore we have further developed our model by taking into account the photon down-scattering on the cold electrons in the wind. For an almost optically thick wind we identify a combination of ejection features and wind parameters that yield bursts with an average power spectrum in agreement with the observations, and with an efficiency of converting the wind kinetic energy in 50-300 keV emission of order 1%. For the same set of model features the interval time between peaks and pulse fluences have distributions consistent with the log-normal distribution observed in real bursts.Comment: ApJ in press, 2000; with slight revisions; 12 pag, 6 fi

Efficiency and spectrum of internal gamma-ray burst shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20 %, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/s is the wind luminosity. For a high, >10 %, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit to wind Lorenz factor and the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energies are set by Thomson optical depth due to electron positron pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.Comment: 10 pages, 5 ps-figures. Expanded discussion of magnetic field and electron energy fraction. Accepted for publication in Astrophysical Journa

Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology

The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin-Voigt, Maxwell, Zener, anti-Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.Comment: 41 pages, 8 figure